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Question 125

The volume of a colloidal particle, $$V_C$$ as compared to the volume of a solute particle in a true solution $$V_s$$, could be

Solution

For a valid comparison we must first recall the usual size ranges of dispersed particles in the two systems.

True solution (molecular dispersion):
Typical solute particle diameter $$d_s$$ is of the order $$0.1\text{ nm-}1\text{ nm}$$ $$\left(10^{-10}\text{-}10^{-9}\ \text{m}\right)$$.

Colloidal solution:
Typical colloidal particle diameter $$d_C$$ lies between $$1\text{ nm-}1000\text{ nm}$$ $$\left(10^{-9}\text{-}10^{-6}\ \text{m}\right)$$. For most common lyophobic and lyophilic sols, the value is nearer the lower edge, i.e. $$\sim 10\text{ nm}$$.

Volume varies as the cube of the diameter:
$$\frac{V_C}{V_s}=\left(\frac{d_C}{d_s}\right)^3$$

Taking representative mid-point values
$$d_C \approx 10\ \text{nm}, \qquad d_s \approx 1\ \text{nm}$$

$$\therefore\ \frac{V_C}{V_s}= \left(\frac{10}{1}\right)^3 = 10^3$$

Hence the volume of a colloidal particle is roughly one thousand times the volume of a solute particle present in a true solution.

Option D which is: $$\frac{V_C}{V_s} \simeq 10^3$$

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